What is the value of q ?
2 answers:
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<h3>Answer: See the diagram below</h3>
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Explanation:
Start at "2" on the number line. If you move to the right 6 steps, each time landing on a tickmark, then you'll arrive at "3" on the number line. This means the interval from 2 to 3 is cut into 6 equal pieces.
In other words, the little tickmarks represent 1/6 of a unit
If we go back to "2" on the number line, and move to the first tickmark, then we arrive at 2 & 1/6. Then the next tickmark would be 2 & 2/6, and so on.
Note how 2/6 = 1/3
So the mixed number 2 & 2/6 = 2 & 1/3
The location of 2 & 1/3 is marked in red in the diagram below.
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The mixed number 1 & 5/6 will be plotted a similar way.
Start at "1" on the number line. Count out 5 spaces until you arrive at 1 & 5/6. This is marked in blue in the same diagram. A shorter way is to start at "2" and count backward 1 tickmark. This works because the "2" is really 1 & 6/6. Going backward one tickmark has that "6/6" bump down to "5/6".
The maximum revenue would be $9600 and would be achieved using 0 nonstop flights and 12 two-stop flights.
<h3>How to define the variables</h3>Let x = number of non-stop airplanes
Let y = number of two-stop airplanes
<h3>The system of linear inequalities</h3>Using the variables in (a), we have the following constraints
Total passenger constraint: 150x + 100y <= 1500
Total Airplanes constraint: x + y <= 12
<h3>Graph the feasible region.</h3>In (b), we have the following system of linear inequalities
150x + 100y <= 1200
x + y <= 12
See attachment for the graph
<h3>The objective function</h3>The objective function of the constraints is:
Max z = 1100x + 800y
<h3>The maximum revenue</h3>From the graph of the function, the optimal solution is:
(x,y) = (0,12)
So, the maximum revenue is:
z = 1100x + 800y
z = 1100*0 + 800*12
z = 9600
Hence, the maximum revenue is $9600
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